Prepared by Johns Hopkins ID Dynamics Working Group
Updated 2020-07-08

FOR PLANNING PURPOSES ONLY: NOT A FORECAST

We compared 3 intervention scenarios for model simulations from January 31, 2020 through December 31, 2020:

[CHANGE BELOW DETAILS ABOUT INTERVENTIONS]

  1. Lockdown followed by Worst-Case Uncontrolled Spread: This scenario has statewide school closures from March 13-19 followed by a statewide stay-at-home policy from March 19 through May 14. All interventions are then removed (back to worst-case uncontrolled transmission) starting May 15.

  2. Lockdown followed by Test and Isolate: This scenario has statewide school closures from March 13-19 followed by a statewide stay-at-home policy from March 19 through May 14. From May 15 through December 31, there is a targeted test and isolate strategy similar to that implemented in South Korea.

  3. Lockdown followed by Moderate Social Distancing: This scenario has statewide school closures from March 13-19 followed by a statewide stay-at-home policy from March 19 through May 14. From May 15 through December 31, there is moderately restrictive social distancing similar to that in US cities during the 1918 influenza pandemic.

[MAYBE WE SHOULD THEN ADD SOME SUMMARY STATEMENTS ABOUT OUR FINDINGS?]

[ALTER BELOW DESCRIPTIVE STRING FOR SCENARIO CAPTIONS]

**Fig. 1**: Daily hospital occupancy for 15 simulation realizations for three scenarios with 8-week lockdown followed by 1) worst-case uncontrolled spread, 2) targeted testing and isolation, and 3) moderately restrictive social distancingat 1 % IFR assumptions.

Fig. 1: Daily hospital occupancy for 15 simulation realizations for three scenarios with 8-week lockdown followed by 1) worst-case uncontrolled spread, 2) targeted testing and isolation, and 3) moderately restrictive social distancingat 1 % IFR assumptions.

What are the features of the planning model?

The model estimates the potential impact of non-pharmaceutical intervention scenarios that governments are using in response to the COVID-19 pandemic. By accounting for factors that help explain how the coronavirus that causes COVID-19 spreads through communities, such as volume of travel in and out of the county and movement within the county, the model provides reasonable estimates about how health outcomes (e.g., epidemic peak timing, hospital bed needs) may be impacted by each of the non-pharmaceutical interventions. These health impact estimates reflect information about local resources and capacity. The models are not predictions, but rather our best approximation of how the COVID-19 pandemic could play out under different government actions. As such, they should be used as decision making tools only; these estimates are not meant to be shared outside of decision-making contexts.

Forecasting models vs planning models

What is the difference?

The difference is important. This report presents planning models tailored to a specific location, with the aim of providing a best estimate of what may happen under different interventions. In contrast, forecasting models attempt to predict what will happen.

Why does that difference matter?

Planning models are a tool for decision makers who are responsible for making decisions about the jurisdictions they serve. They are less useful for members of the general public who are not making decisions for their cities. The different scenarios used in planning models assume that the government actions will result in large-scale behavior change that is best accomplished through government action, and can inform resource allocation decisions made by governments and healthcare organizations.

State Level Results

Summary

Tab.1: Summary acrossthree scenarios with 8-week lockdown followed by 1) worst-case uncontrolled spread, 2) targeted testing and isolation, and 3) moderately restrictive social distancing. Estimates are presented across4time periods for 1% infection fatality ratio (IFR) assumptions.

Jan 30-Jun 01

Jan 30-Jun 01

Jun 01-Jul 01

Jun 01-Jul 01

Jul 01-Aug 01

Jul 01-Aug 01

Aug 01-Jan 30

Aug 01-Jan 30

mean

95% PI

mean

95% PI

mean

95% PI

mean

95% PI

Infections in Period

Lockdown followed by Moderate Social Distancing

159,400

18,640-416,430

486,150

213,210-635,770

156,410

14,190-427,310

23,600

190-100,430

Lockdown followed by Test and Isolate

109,490

14,310-232,030

467,980

189,830-639,820

205,500

38,970-459,930

26,540

620- 99,700

Lockdown followed by Worst Case Uncontrolled Spread

369,500

55,270-661,520

340,210

190,470-519,890

96,180

2,930-333,080

10,770

20- 45,110

Deaths in Period

Lockdown followed by Moderate Social Distancing

380

30-1,300

3,710

710-6,060

3,430

1,130-5,890

760

10-3,030

Lockdown followed by Test and Isolate

190

40- 470

3,120

520-5,470

3,840

2,450-4,940

910

50-3,000

Lockdown followed by Worst Case Uncontrolled Spread

940

120-1,830

4,830

1,590-6,530

2,010

290-4,400

400

0-1,610

Hospital Admissions in Period

Lockdown followed by Moderate Social Distancing

10,050

1,150-29,530

48,650

17,360-68,600

20,310

2,800-44,850

3,540

50-14,800

Lockdown followed by Test and Isolate

6,400

920-14,250

44,880

13,280-67,760

25,740

7,300-47,360

4,080

120-14,900

Lockdown followed by Worst Case Uncontrolled Spread

27,600

3,460-52,010

40,070

25,560-55,610

12,360

630-38,760

1,640

10- 6,800

Peak Hospital Occupancy in Period

Lockdown followed by Moderate Social Distancing

6,310

670-16,530

26,190

10,660-34,270

19,200

7,640-30,820

3,870

120-14,520

Lockdown followed by Test and Isolate

4,470

560- 9,610

22,470

8,560-32,200

20,250

16,470-22,780

4,970

350-15,380

Lockdown followed by Worst Case Uncontrolled Spread

18,230

2,330-34,220

26,160

15,050-35,040

10,530

2,070-18,210

2,240

20- 8,780

ICU Admissions in Period

Lockdown followed by Moderate Social Distancing

1,190

100- 4,130

11,840

2,280-19,110

10,850

3,700-18,550

2,430

60- 9,510

Lockdown followed by Test and Isolate

620

120- 1,470

10,010

1,720-17,650

12,290

7,960-15,960

2,990

170- 9,870

Lockdown followed by Worst Case Uncontrolled Spread

2,970

350- 5,700

15,430

5,070-20,690

6,430

900-14,060

1,280

10- 5,130

Peak ICU Occupancy in Period

Lockdown followed by Moderate Social Distancing

960

80- 3,340

8,980

1,940-14,650

12,110

8,210-14,900

3,480

420- 7,990

Lockdown followed by Test and Isolate

490

80- 1,150

7,770

1,450-13,480

11,250

8,630-14,300

4,650

1,100- 8,760

Lockdown followed by Worst Case Uncontrolled Spread

2,690

290- 5,300

10,960

3,880-15,440

8,530

6,160-10,990

2,200

100- 7,250

Incident Ventilations in Period

Lockdown followed by Moderate Social Distancing

50

0- 4,130

780

100-19,110

2,380

1,130-18,550

770

50- 9,510

Lockdown followed by Test and Isolate

20

0- 1,470

550

70-17,650

2,310

1,070-15,960

990

150- 9,870

Lockdown followed by Worst Case Uncontrolled Spread

60

10- 5,700

1,810

290-20,690

1,610

800-14,060

460

10- 5,130

Peak Ventilators in Use in Period

Lockdown followed by Moderate Social Distancing

40

0- 160

630

80-1,410

1,800

890-2,250

1,110

320-1,970

Lockdown followed by Test and Isolate

20

0- 50

470

60- 980

1,590

820-2,170

1,200

790-1,540

Lockdown followed by Worst Case Uncontrolled Spread

50

10- 90

1,370

250-2,400

1,780

1,180-2,360

620

80-1,310

Diversity of Possible Outcomes

**Fig. 1 **: Distribution of cumulative hospital admissions for three scenarios with 8-week lockdown followed by 1) worst-case uncontrolled spread, 2) targeted testing and isolation, and 3) moderately restrictive social distancing at 1% IFR assumptions. Each bar represents a bin of 2,000 hospitalizations.

Fig. 1 : Distribution of cumulative hospital admissions for three scenarios with 8-week lockdown followed by 1) worst-case uncontrolled spread, 2) targeted testing and isolation, and 3) moderately restrictive social distancing at 1% IFR assumptions. Each bar represents a bin of 2,000 hospitalizations.

Boxplots for State Level Results

Scenario Summaries

Scenario 1: Lockdown followed by Worst-Case Uncontrolled Spread

  1. Lockdown followed by Worst-Case Uncontrolled Spread: This scenario has statewide school closures from March 13-19 followed by a statewide stay-at-home policy from March 19 through May 14. All interventions are then removed (back to worst-case uncontrolled transmission) starting May 15.

Tab. 2 State-level summary for Lockdown followed by Worst Case Uncontrolled Spread scenario reported for the period from 2020-1-31 through the dates specified by the column headers.

IFR

Jun 01
mean


95% PI

Jul 01
mean


95% PI

Aug 01
mean


95% PI

INFECTIONS

387,100

(60,400-683,400)

715,500

(407,500-852,400)

806,800

(728,300-854,900)

HOSPITALIZATIONS
total

0.25% IFR

7,400

( 900-13,800)

17,100

( 8,100-21,100)

20,000

(17,600-21,300)

0.5% IFR

14,800

(1,900-27,900)

34,100

(16,300-42,700)

40,000

(35,300-43,000)

1% IFR

29,500

(3,800-55,100)

68,400

(32,900-84,800)

80,200

(70,700-85,300)

daily peak admissions

0.25% IFR

500

(100- 900)

700

( 400- 900)

700

( 400- 900)

0.5% IFR

1,000

(200-1,700)

1,300

( 800-1,700)

1,300

( 900-1,700)

1% IFR

2,000

(400-3,400)

2,600

(1,600-3,400)

2,600

(1,800-3,400)

daily peak capacity

0.25% IFR

4,700

( 600- 8,700)

6,600

( 3,800- 8,800)

6,800

( 4,700- 8,800)

0.5% IFR

9,400

(1,300-17,600)

13,200

( 7,700-17,700)

13,600

( 9,500-17,700)

1% IFR

18,900

(2,600-34,800)

26,300

(15,500-35,000)

27,000

(18,800-35,000)

ICU
total

0.25% IFR

900

(100-1,600)

4,700

(1,400- 6,600)

6,200

( 4,900- 6,800)

0.5% IFR

1,700

(200-3,300)

9,400

(2,900-13,400)

12,500

( 9,900-13,800)

1% IFR

3,400

(400-6,500)

18,700

(5,800-26,500)

24,900

(19,800-27,300)

daily peak admissions

0.25% IFR

100

(10-200)

200

(100- 300)

200

(200- 300)

0.5% IFR

200

(20-400)

400

(200- 600)

400

(300- 600)

1% IFR

400

(40-800)

800

(400-1,100)

900

(600-1,100)

daily peak capacity

0.25% IFR

800

(100-1,500)

2,700

(1,000- 3,800)

3,000

(2,200- 3,800)

0.5% IFR

1,500

(200-3,000)

5,600

(2,000- 7,800)

6,100

(4,300- 7,800)

1% IFR

3,000

(300-6,000)

11,000

(4,100-15,400)

12,000

(8,600-15,400)

DEATHS
total

0.25% IFR

300

( 30- 500)

1,500

( 500-2,100)

2,000

(1,600-2,100)

0.5% IFR

500

( 60-1,000)

2,900

( 900-4,100)

3,800

(3,100-4,200)

1% IFR

1,100

(130-2,100)

5,900

(1,800-8,300)

7,800

(6,200-8,500)

**Fig. 2 ** County-level map of infections per 10,000 for Lockdown followed by Worst Case Uncontrolled Spread strategy.

Fig. 2 County-level map of infections per 10,000 for Lockdown followed by Worst Case Uncontrolled Spread strategy.

Scenario 2: Lockdown followed by Test and Isolate

  1. Lockdown followed by Test and Isolate: This scenario has statewide school closures from March 13-19 followed by a statewide stay-at-home policy from March 19 through May 14. From May 15 through December 31, there is a targeted test and isolate strategy similar to that implemented in South Korea.

Tab. 3 State-level summary for Lockdown followed by Test and Isolate scenario reported for the period from 2020-1-31 through the dates specified by the column headers.

IFR

Jun 01
mean


95% PI

Jul 01
mean


95% PI

Aug 01
mean


95% PI

INFECTIONS

121,200

(15,800-254,000)

589,500

(218,500-810,200)

785,100

(671,900-847,900)

HOSPITALIZATIONS
total

0.25% IFR

1,800

( 300- 4,000)

13,000

( 3,700-19,400)

19,100

(15,400-21,000)

0.5% IFR

3,600

( 500- 8,000)

26,200

( 7,700-39,100)

38,500

(31,300-42,500)

1% IFR

7,100

(1,000-15,800)

52,700

(15,300-78,500)

77,300

(62,700-85,000)

daily peak admissions

0.25% IFR

200

(20- 400)

600

( 300- 800)

600

( 500- 800)

0.5% IFR

400

(50- 800)

1,100

( 600-1,600)

1,200

(1,000-1,600)

1% IFR

800

(90-1,600)

2,300

(1,100-3,100)

2,400

(1,900-3,100)

daily peak capacity

0.25% IFR

1,300

(200- 2,700)

5,600

(2,300- 7,900)

6,200

( 5,000- 7,900)

0.5% IFR

2,500

(300- 5,400)

11,200

(4,600-16,000)

12,600

(10,300-16,000)

1% IFR

5,000

(600-10,700)

22,700

(9,200-32,200)

25,400

(20,400-32,200)

ICU
total

0.25% IFR

200

( 30- 400)

2,800

( 500- 4,900)

5,700

( 3,600- 6,700)

0.5% IFR

400

( 60- 800)

5,600

(1,000- 9,900)

11,600

( 7,600-13,600)

1% IFR

700

(120-1,600)

11,200

(2,000-19,900)

23,100

(15,000-27,100)

daily peak admissions

0.25% IFR

20

(10- 40)

200

( 30- 300)

200

(200- 300)

0.5% IFR

30

(10- 70)

300

( 90- 500)

400

(300- 500)

1% IFR

60

(10-130)

600

(170-1,000)

800

(600-1,000)

daily peak capacity

0.25% IFR

100

(20- 300)

2,000

( 300- 3,400)

2,800

(2,200- 3,500)

0.5% IFR

300

(50- 700)

4,000

( 800- 6,900)

5,600

(4,500- 7,100)

1% IFR

500

(90-1,200)

8,000

(1,600-13,800)

11,300

(8,800-14,300)

DEATHS
total

0.25% IFR

100

(10-100)

900

(100-1,500)

1,800

(1,200-2,100)

0.5% IFR

100

(20-200)

1,800

(300-3,100)

3,600

(2,400-4,300)

1% IFR

200

(40-500)

3,500

(600-6,200)

7,200

(4,800-8,400)

**Fig. 3 ** County-level map of infections per 10,000 for Lockdown followed by Test and Isolate strategy.

Fig. 3 County-level map of infections per 10,000 for Lockdown followed by Test and Isolate strategy.

Scenario 3: Lockdown followed by Moderate Social Distancing

  1. Lockdown followed by Moderate Social Distancing: This scenario has statewide school closures from March 13-19 followed by a statewide stay-at-home policy from March 19 through May 14. From May 15 through December 31, there is moderately restrictive social distancing similar to that in US cities during the 1918 influenza pandemic.

Tab. 4 State-level summary for Lockdown followed by Moderate Social Distancing scenario reported for the period from 2020-1-31 through the dates specified by the column headers.

IFR

Jun 01
mean


95% PI

Jul 01
mean


95% PI

Aug 01
mean


95% PI

INFECTIONS

173,800

(20,600-442,300)

655,500

(266,400-829,100)

803,800

(687,100-846,200)

HOSPITALIZATIONS
total

0.25% IFR

2,800

( 300- 8,000)

14,900

( 4,900-20,200)

19,600

(16,000-21,000)

0.5% IFR

5,500

( 600-15,800)

30,000

( 9,900-40,500)

39,700

(32,100-42,700)

1% IFR

11,000

(1,300-31,700)

60,000

(19,800-81,500)

79,300

(64,400-84,700)

daily peak admissions

0.25% IFR

200

( 30- 500)

700

( 300- 800)

700

( 500- 800)

0.5% IFR

500

( 50-1,100)

1,300

( 600-1,700)

1,400

( 900-1,700)

1% IFR

1,000

(110-2,100)

2,600

(1,200-3,400)

2,800

(1,900-3,400)

daily peak capacity

0.25% IFR

1,700

(200- 4,400)

6,500

( 2,700- 8,500)

7,000

( 4,800- 8,500)

0.5% IFR

3,500

(400- 8,800)

13,300

( 5,600-17,400)

14,200

( 9,600-17,400)

1% IFR

7,000

(700-17,600)

26,400

(11,100-34,300)

28,300

(19,300-34,400)

ICU
total

0.25% IFR

300

( 30-1,200)

3,400

( 700- 5,800)

5,900

( 4,000- 6,700)

0.5% IFR

700

( 40-2,300)

6,800

(1,300-11,700)

12,000

( 7,900-13,600)

1% IFR

1,300

(110-4,400)

13,600

(2,700-23,500)

24,000

(15,800-26,900)

daily peak admissions

0.25% IFR

30

( 0-100)

200

(100- 300)

200

(200- 300)

0.5% IFR

60

(10-200)

400

(100- 600)

500

(300- 600)

1% IFR

110

(10-300)

800

(200-1,100)

900

(600-1,100)

daily peak capacity

0.25% IFR

300

(20- 900)

2,300

( 500- 3,600)

3,000

(2,100- 3,700)

0.5% IFR

500

(30-1,800)

4,600

(1,100- 7,400)

6,200

(4,200- 7,500)

1% IFR

1,000

(90-3,600)

9,200

(2,100-14,700)

12,400

(8,400-14,900)

DEATHS
total

0.25% IFR

100

(10- 300)

1,100

(200-1,900)

1,900

(1,300-2,100)

0.5% IFR

200

(20- 700)

2,100

(500-3,700)

3,800

(2,500-4,300)

1% IFR

400

(40-1,400)

4,300

(800-7,400)

7,600

(5,000-8,500)

**Fig. 4 ** County-level map of infections per 10,000 for Lockdown followed by Moderate Social Distancing strategy.

Fig. 4 County-level map of infections per 10,000 for Lockdown followed by Moderate Social Distancing strategy.

County-Specific Results

New Castle

Tab. 5 : Summary across three scenarios with 8-week lockdown followed by 1) worst-case uncontrolled spread, 2) targeted testing and isolation, and 3) moderately restrictive social distancing for the county of New Castle . Estimates are presented across 4 time periods for 1% IFR assumptions.

Jan 30-Jun 01

Jan 30-Jun 01

Jun 01-Jul 01

Jun 01-Jul 01

Jul 01-Aug 01

Jul 01-Aug 01

Aug 01-Jan 30

Aug 01-Jan 30

mean

95% PI

mean

95% PI

mean

95% PI

mean

95% PI

Infections in Period

Lockdown followed by Moderate Social Distancing

66,900

4,100-168,400

303,600

87,900-395,100

105,700

11,700-289,100

19,500

200- 83,900

Lockdown followed by Test and Isolate

31,900

7,300- 75,600

293,200

117,600-421,500

145,100

31,800-277,600

15,800

500- 55,400

Lockdown followed by Worst Case Uncontrolled Spread

184,300

17,500-362,100

225,000

143,500-341,400

71,600

2,300-244,000

8,800

0- 36,900

Deaths in Period

Lockdown followed by Moderate Social Distancing

0

0- 100

1,100

100-2,000

1,100

500-1,800

300

0-1,200

Lockdown followed by Test and Isolate

0

0- 0

700

200-1,500

1,400

1,000-1,800

300

0- 900

Lockdown followed by Worst Case Uncontrolled Spread

100

0- 300

1,400

300-2,100

700

100-1,300

200

0- 700

Hospital Admissions in Period

Lockdown followed by Moderate Social Distancing

1,700

100- 4,500

15,000

3,200-21,000

6,600

1,100-14,000

1,400

0- 6,100

Lockdown followed by Test and Isolate

800

200- 1,900

13,000

4,100-20,900

9,200

3,000-14,500

1,200

0- 4,200

Lockdown followed by Worst Case Uncontrolled Spread

6,300

500-13,200

13,000

5,700-17,500

4,500

200-13,700

700

0- 2,900

Peak Hospital Occupancy in Period

Lockdown followed by Moderate Social Distancing

1,400

100- 3,500

8,300

2,200-10,600

6,600

3,200- 9,700

1,500

100- 5,600

Lockdown followed by Test and Isolate

600

100- 1,500

7,300

2,700-10,700

7,200

6,200- 8,600

1,600

100- 4,400

Lockdown followed by Worst Case Uncontrolled Spread

4,800

400-10,100

8,200

3,700-11,500

3,800

800- 6,200

900

0- 3,500

ICU Admissions in Period

Lockdown followed by Moderate Social Distancing

100

0- 300

3,400

400-6,200

3,500

1,500-5,800

1,000

0-3,800

Lockdown followed by Test and Isolate

100

0- 200

2,400

500-4,800

4,400

3,100-5,900

900

100-2,800

Lockdown followed by Worst Case Uncontrolled Spread

500

0-1,000

4,600

1,000-7,000

2,200

400-4,300

500

0-2,100

Peak ICU Occupancy in Period

Lockdown followed by Moderate Social Distancing

100

0- 300

2,700

300-4,500

3,900

2,500-4,600

1,200

100-2,800

Lockdown followed by Test and Isolate

100

0- 100

2,000

400-4,000

3,800

2,700-4,700

1,700

500-2,700

Lockdown followed by Worst Case Uncontrolled Spread

500

0-1,000

3,400

800-5,000

3,000

2,400-3,500

800

0-2,600

Incident Ventilations in Period

Lockdown followed by Moderate Social Distancing

0

0- 300

200

0-6,200

700

200-5,800

300

0-3,800

Lockdown followed by Test and Isolate

0

0- 200

100

0-4,800

700

300-5,900

300

0-2,800

Lockdown followed by Worst Case Uncontrolled Spread

0

0-1,000

500

0-7,000

500

300-4,300

200

0-2,100

Peak Ventilators in Use in Period

Lockdown followed by Moderate Social Distancing

0

0- 0

200

0-400

600

200-700

400

100-600

Lockdown followed by Test and Isolate

0

0- 0

100

0-200

500

300-700

400

300-600

Lockdown followed by Worst Case Uncontrolled Spread

0

0- 0

400

0-800

600

300-800

200

0-400

Boxplots for County Level Results

Appendix 1: Methods

Pipeline Overview

The model results here are the results of a modeling pipeline that moves from a seeding phase, through epidemic simulation, a outcome and hospitalization generation engine, and report generation. Core code for all aspects of the pipeline is all open source. The core pipeline phases are:

  • Seeding: We run a model to determine the likelihood of importing cases into the region of interest. We maintain an R package.

  • Epidemic Simulation: We run a location stratified SEIR model, using a python module in COVIDScenarioPipeline.

  • Hospitalization and Outcome Generator: We estimate secondary effects of infection using infection numbers using the hospitalization R package in COVIDScenarioPipeline.

  • Report Generation: We provide functions to access results and help produce reports in the report_generation R package in COVIDScenarioPipeline.

Technical Details

Data Sources

  • County-level confirmed SARS-COV-2 infections: JHU CSSE COVID-19 Data Portal

  • US Census Bureau 2010 county commuting flows and 2016 population data

Our model and report make the following key assumptions:

  • Mean incubation period: 5.2 days

  • Infectious period: ranges from 2.6-6 days

  • R0: 2-3

  • We examine 3 infection fatality rates (IFR) throughout our report: 0.25, 0.5, 1%.

  • We assume that 10% of all hospitalized patients will die and adjust overall hospitalization rates to match the given IFR for a scenario.

  • Hospitalizations admitted to the ICU: 32%

  • ICU admissions that are ventilated: 15%

Epidemic Simulation

[CHOOSE ONE OF THESE CHUNKS DEPENDING ON SEEDING. POISSON SEEDING TEXT SAYS 10X] <!–

We used a global air importation model in conjunction with global cumulative confirmed COVID case data from JHU CSSE COVID-19 Data Portal and assumptions in recent travel reductions to estimate the number of COVID case importations into major airports located in and surrounding areas (Delaware) from January through March. These estimated global importations were used to seed our epidemic model.

If the number of infections in any single county was below the number of confirmed cases reported by the JHU CSSE COVID-19 Data Portal on a given day between February 1 and March 18, the simulation was stopped and removed from the model results. We ran 1000 model simulations from January 31, 2020 through December 31, 2020 for each scenario. Some outcomes may be reported beyond the simulation period in order to examine the full disease course for infections occurring at the end of the simulation period.

We seeded the epidemic with roughly 10x the number of confirmed cases reported by the JHU CSSE COVID-19 Data Portal for the five days prior to the first confirmed cases into each county in Louisiana. We ran 1000 model simulations from January 31, 2020 through December 31, 2020 for each scenario. Some outcomes may be reported beyond the simulation period in order to examine the full disease course for infections occurring at the end of the simulation period.

Base principle

The epidemiological model is an stochastic spatial ‘SEIR model’ where the population of each node is divided in categories depending on their situation with regard to the diseases. The compartments are:

  • \(S\) Susceptible individuals that may contracts COVID-19.
  • \(E\) Exposed individuals that are incubating the disease, after being in contact with another infected.
  • \(I\) Infected and infectious individuals.
  • \(R\) Recovered individuals with immunity to re-infection.
Dynamics and parameters

In practice, this translate into \(k = 3\) compartments of infected, \(I_1, I_2, I_3\) in order to have an infectious period shaped as Erlang distribution. Then the rates of the different compartments are given in the table below:

Transition rate parameter Unit
\(S\longrightarrow E\) \(\beta = R_0 \cdot \gamma\) d\(^{-1}\)
\(E\longrightarrow I_1\) \(\sigma = \frac{1}{5.2}\) d\(^{-1}\)
\(I_1\longrightarrow I_2\) \(\gamma_1 = \gamma \cdot k\) d\(^{-1}\)
\(I_2\longrightarrow I_3\) \(\gamma_1 = \gamma \cdot k\) d\(^{-1}\)
\(I_3\longrightarrow R\) \(\gamma_1 = \gamma \cdot k\) d\(^{-1}\)

For such epidemiological model, two meta-parameters are important in reproducing the dynamics and final size of an epidemic: the serial interval \(SI\), which is the interval between two subsequent infections, and the basic reproductive number \(R_0\) representing the number of newly infected per infected, in a fully susceptible population.

The serial interval (SI) of COVID-19 is currently estimated to be in range \(6.5-8.2\). We draw uniformly from this range, and we solve \(SI = \frac{1}{2}(\frac{1}{\gamma})+\frac{1}{\sigma}\) for the inverse of the total infectious period, \(\gamma\).

The basic reproductive number, \(R_0\), is drawn for each simulation and we obtain parameter beta from \(\beta= R_0 \cdot \gamma\).

The model is fixed time step, and the transitions (without mobility here) at each time step \(\Delta t\) are:

\[\begin{eqnarray} p_{expose} &=& 1 - \exp(-\Delta t \cdot FOI) \\ p_{infect} &=& 1 - \exp(-\Delta t \cdot \sigma)\\ p_{recover} &=& 1 - \exp(-\Delta t \cdot \gamma) \end{eqnarray}\] At each time step, we draw in a binomial distribution, e.g \[\begin{equation} N_{I_1\longrightarrow I_2}(t) = \text{Binom}(I_1, 1 - \exp(-\Delta t \cdot \gamma_1)) \end{equation}\] The force of infection without mobility is defined as: \[\begin{equation} FOI = \beta \frac{(I_1 + I_2 + I_3)^\alpha}{H} \end{equation}\]

where \(\alpha\) is a coefficient that dampens disease transmission when its value is below 1, thus more accurately representing non-homogeneous mixing in the population. Although we were unable to find \(\alpha\) estimates for SARS-CoV-2, we expect disease transmission to be similar to that of other respiratory diseases and typical estimated values for \(\alpha\) for respiratory diseases range from 0.87 to 0.97. We used an \(\alpha\) value of 1 in these models.

In our model, individuals move from one node to another. A mobility matrix \(M\) where \(M(o,d)\) is the amount of individuals moving daily from origin \(o\) to destination \(d\). At each time step, and for each \((o,d)\) pair, we draw a force of infection for node \(i\) to account for mobility:

\[\begin{eqnarray} FOI_i &=& \left(1 - \sum_{j\neq i} p_{away} \frac{M_{i,j}}{H_i} \right) \cdot \beta_i(t) \frac{(I_1^{i} + I_2^{i} + I_3^{i})^\alpha}{H_i} + \\ && \sum_{j \neq i} \left(p_{away} \frac{M_{i,j}}{H_i} \cdot \beta_j(t) \frac{(I_1^j + I_2^j + I_3^j)^\alpha}{H_j} \right) \end{eqnarray}\]

with \(p_{away}\) the percent of the time individuals that move spend away; \(p_{away} \approx 0.5\) in the case of commuting. \(H_i\) is the population of node \(i\). Then, the transition is:

\[\begin{equation} N_{S_i \longrightarrow I_1^{i}}(t) = Binom(S^i, 1 - \exp(-\Delta t \cdot FOI_i)) \end{equation}\]

The model is implemented in python, just-in-time compiled to machine code using Numba.

Limitations

We note several limitations to our work:

  1. We truncated the initial run of these simulations on December 31, 2020. Our estimates therefore do not necesarily represent a total or final outbreak size in all scenarios. This truncation also has implications for the estimated number of hospitalizations and deaths, as many individuals have yet to reach their final outcome by December 31, 2020.

  2. There remains considerable uncertainty around some of the key epidemiologic features of COVID-19, including the average duration of infectiousness and time to recovery or death. We have used commonly accepted and well supported estimates, in line with those recommended by the CDC, of these parameters and believe that they are appropriate for planning purposes.

  3. We assume equal risk of infection and progression to hospitalization or death among all individuals within a county at a given time point. There is evidence of age-specific differences in clinical burden and perhaps in susceptibility to infection that are not considered here. Counties with older populations may experience a higher burden of clinical cases requiring hospitalization or ICU admission.

  4. We assume \(R_e\), the effective reproductive number, to be constant in each scenario, other than changes due to onset of non-pharmaceutical interventions. As capacity for surveillance, contact tracing, and testing improve, and as the general public becomes increasingly aware of the outbreak and modifies their own behavior, we might expect that \(R_e\) will decrease dynamically, perhaps even as a function of the perceived COVID19 burden. As the outbreak continues, it will be possible to refine the scenarios considered here to better reflect the actual epidemic situation.

  5. We do not explicitly model the role of asymptomatic infection when calculating the number of expected hospitalizations. All infectious individuals are considered at risk of hospitalization, though some may recover or die prior to hospitalization. A substantial asymptomatic burden may reduce the number of hospitalized cases.

Key Sources

  • Impact of broad scale non-pharmaceutical intervetions is based on the observed impact of such programs in 1918 as reported in (Bootsma and Ferguson 2007). We took parameter estimates on the effectiveness of interventions from Milwaukee in this study.

  • School closure impacts based on data from (Jackson et al. 2020), (Cauchemez et al. 2008) and (Litvinova et al. 2019)

  • Approximate generation time is based on data from (Bi et al. 2020)

  • Range of \(R_0\) selected to be consistent with the early stages of the Wuhan epidemic and is broadly consistent with estimates from Imperial College (https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-2019-nCoV-transmissibility.pdf), (Riou and Althaus 2020), (Majumder and Mandl 2020), (Zhao et al. 2020)

  • Assumption on ICU occupancy in the United States (Halpern and Pastores 2015)

  • Estimates of the transmission dampening parameter \(\alpha\) range from 0.87 to 0.97 for respiratory viruses from (Metcalf et al. 2011), (Word et al. 2012), (Finkenstadt, Bjornstad, and Grenfell 2002), (Becker and Grenfell 2017)

Development Team

[ADD NAMES AND RECOMPILE PACKAGE AS NECESSARY]

This report would not be possible without the work of the COVID-19 Scenario Modeling Pipeline Working Group:

EPFL

Johns Hopkins Infectious Disease Dynamics

University of Utah

Developers Without Affiliation

Amazon Web Services

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